Common Hypercyclic Vectors and the Hypercyclicity Criterion |
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Authors: | Rebecca Sanders |
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Institution: | 1. Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI, 53201, USA
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Abstract: | An operator on a separable, infinite dimensional Banach space satisfies the Hypercyclicity Criterion if and only if the associated
left multiplication operator is hypercyclic; see 14], 16], 29]. By examining paths of operators where each operator along
the path satisfies the criterion, we provide necessary and sufficient conditions for a path of left multiplication operators
to have an SOT-dense set of common hypercyclic vectors. As a corollary, we establish a natural sufficient condition for a
path of operators to have a common hypercyclic subspace. |
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Keywords: | |
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